The objective function in (REF ) has a typical expression of weighted sum-of-logarithmic functions of SINR\(_k\) , which makes the optimization problem (REF ) intractable. Motivated by the closed-form FP algorithm introduced in [1]}, [2]}, we attempt to equivalently transform the original problem into a sum-of-ratios form by extracting the ratio terms SINR\(_k\) , \(k \in \mathcal {K},\)  from the logarithmic function.
Based on Lagrangian dual transform [1]}, the optimization problem (REF ) is equivalent to
